Endodontic Instrument With Enlarged Chip Space And Reduced Torque Strength

ABSTRACT

An endodontic instrument of this disclosure has less torque strength but greater flexibility and enlarged chip space compared to the prior art. In embodiments. only two flutes are spiraled about the instrument&#39;s length L to form two non-landed cutting edges between D2 and D16, the cutting edges merging to form a land at about D1. The tip end is rounded. The helical angle α increases from the handle end toward the tip end, a number of spirals per unit length being at least two times greater toward the tip end than toward the handle end, a cross-section of the length L consisting of two convex portions intersecting at each cutting edge or a wave-shape having one concave portion and one convex portion intersecting at each cutting edge, the cross-section occupying less total area than would a same size endodontic instrument having a triangular cross-section and providing greater chip space.

CROSS REFERENCE TO CO-PENDING APPLICATIONS

This application is a continuation of U.S. application Ser. No.17/688,446, filed Mar. 7, 2022, the content of which is incorporated byreference herein.

BACKGROUND

This disclosure is in the field of rotary endodontic instruments made ofnickel-titanium, or a material with similar properties, and used toclean and shape a root canal. The instrument may be configured as a fileor a reamer. See American Association of Endodontists, Glossary ofEndodontic Terms (9th Ed.) for a definition of these terms, the contentof which is incorporated by reference herein.

Endodontic rotary files fail from either torque or cyclic fatigue.Historically, the vast majority of failures are due to cyclic fatigue.Regardless of the cause, most failures occur within the first 4 mm or 5mm of the file, which is the apical end of the file. For example,torsional fatigue most often occurs when the tip of the instrument bindsin the root canal as the remaining length of the shaft continues torotate.

The torsional and flexural stiffness of nickel-titanium (“NiTi”)endodontic rotary files is discussed in Seung Ho Baek et al., Comparisonof Torsional Stiffness of Nickel-Titanium Rotary Files with DifferentGeometric Characteristics, 37 J. Endodontics 1283 (No. 9, Sep. 2011);Antheunis Versluis et al., Flexural Stiffness and Stresses inNickel-Titanium Rotary Files for Various Pitch and Cross-sectionalGeometries, 38 J. Endodontics 1399 (No. 10, Oct. 2012); and AlessioZanza et al., A Paradigm Shift for Torsional Stiffness ofNickel-Titanium Rotary Instruments: A Finite Element Analysis, 47 J.Endodontics 1149 (No. 7, July 2021), the content of each is incorporatedby reference herein. The cross-sectional geometry of the prior artrotary files discussed include those with a triangular cross section, askinny rectangle, and a fat rectangle, off-centered, and changing in twodimensions (length and width) along the length of the file.

Prior art file design is primarily a trade-off between torsionalstrength and flexibility, with increased torsional strength desirable toreduce or eliminate the potential for breakage. Torsional strength canbe increased by reducing the pitch (increasing the number of threads orspirals per unit of length) and increasing the cross-sectional areasalong the length of the file. The cross-sectional area along the lengthof prior art files with a triangular cross-section is no less than 40%of the total area of its circle of rotation, and for square orrectangular cross-section no less than 60% of the total area of thecircle of rotation. The circle of rotation lies in a plane orthogonal tothe longitudinal axis of the file and has a diameter defined by thecutting edges at the cross-section.

Cross-sectional design is “one of the most important parameters thatcharacterizes torsional stiffness . . . because it deeply influencesmechanical properties.” See Zanza et al. ar 1149. Two instruments with adifferent cross-sectional shape but the same cross-sectional area can“develop different torsional resistance because of their differentgeometry.” Id. at 1150. “[T]he bigger the mass and volume/mm of theinstrument, the more its stiffness increases, and the more its fatigueresistance decreases, causing the instrument to withstand worser withflexural stresses.” Id. Therefore, what is needed is an endodonticinstrument that has a reduced cross section relative to a triangularcross-section, more flexibility but reduced torque strength, and canstill shape a root canal without breaking within the canal.

SUMMARY

Embodiments of an endodontic instrument of this disclosure have across-section along its working (bladed or cutting edge) length thatprovides less torque strength but more flexibility than an endodonticinstrument having a triangular-, square, or rectangular-shapedcross-section. The mass of metal at each cross-section diameter of theinstrument is less than that of a triangle-shaped cross-section for asame, corresponding size of endodontic instrument. Additionally, thecore diameter of the working length is less than that of thetriangular-shaped cross-section.

In embodiments, the cross-section includes only two cutting edges, thecross-section having opposing and convex portions intersecting at eachcutting edge or a convex portion intersecting an opposing concaveportion at each cutting edge. At each diameter along the working length,the cross-section of the instrument occupies about 20% of the total areaA to less than that occupied by a triangle, 25% to less than thatoccupied by a triangle, 30% to less than that occupied by a triangle,35% to less than that occupied by a triangle, there being sub-ranges anddiscrete values within these broader ranges. This reducedcross-sectional area provides an enlarged chip space, thereby allowingthe instrument, despite its reduced torque strength, to maintain itsintegrity and not break during use.

The tip end of an endodontic instrument of this disclosure may beshovel-shaped, the shovel shape beginning at about the D2 diameter, thatis, about 2 mm from the tip end, with each cutting edge merging into thecore in between the D1 and D0 diameter to form a radial land.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plan view of an embodiment of an endodontic instrument ofthis disclosure. The cross-section has opposing and convex portionsintersecting at each cutting edge, there being only two cutting edges.The enlarged chip space provided compensates for the reduced torquestrength. In embodiments, the helical angle α increases from theproximal end to the distal end as does the number of spirals.

FIGS. 2-7 are cross-section views each taken along their respectivesection lines of FIG. 1 . The cross-section views show the path P ofeach cutting edge as it ever slightly decreases its distance from theaxial centerline.

FIG. 8 is a plan view of another embodiment of an endodontic instrumentof this disclosure. The cross-section has a convex portion intersectingan opposing concave portion at each cutting edge and provides two sharpedges to help prevent binding between the instrument and the canal wall.The enlarged chip space provided compensates for the reduced torquestrength. The helical angle α and number of spirals may vary like thatof the instrument of FIG. 1 .

FIGS. 9-10 are cross-section views taken along respective section linesof FIG. 8 . The cross-section views show the path P of each cutting edgeas it ever slightly decreases its distance from the axial centerline.

FIG. 11 is an end view of the embodiment of FIG. 1 .

FIG. 12 is cross-section view of the embodiment of FIG. 8 , illustratinga circle of rotation and chip space between cutting edges within it.

FIG. 13 is a cross-section view of a prior art endodontic instrumenthaving a triangular cross-section and illustrating the circle ofrotation and chip space between cutting edges within it. Embodiments ofthis disclosure provide a greater amount of chip space than does atriangular cross-section.

DEFINITIONS

Total area “A”: the area defined by a circle of rotation at eachdiameter along the working length of the endodontic instrument,

ΠR ²  (Eq. 1)

where R is the radius of the circle of rotation.

Circle of Rotation “C”: a circle lying in a plane orthogonal to thelongitudinal axis of the endodontic instrument and containing acorresponding one of the diameters of the endodontic instrument, thecircle of rotation having a diameter defined by a line passing throughthe longitudinal axis and having as its endpoints the two cutting edgesof the endodontic instrument.

Cross-section area “a”: the area occupied by the endodontic instrumentwithin the circle of rotation, where A>a. For a triangular cross-sectioninscribed with a circle of rotation C having a radius R, the area a is

$\begin{matrix}{\frac{3\sqrt{3}}{4}R^{2}} & \left( {{Eq}.2} \right)\end{matrix}$

which, when simplified, is about 1.3 R². Therefore, the percentage oftotal area A occupied by a triangular cross section is calculated asfollows:

$\begin{matrix}{\frac{\frac{3\sqrt{3}}{4}R^{2}}{\Pi R^{2}} \times 100{or}} & \left( {{Eq}.3} \right)\end{matrix}$ $\begin{matrix}{\frac{3\sqrt{3}}{4\Pi} \times 100} & \left( {{Eq}.4} \right)\end{matrix}$

which, when simplified, is about 41%. For a square cross-section, Abecomes:

2R ²  (Eq. 5)

Therefore, a triangular cross-section occupies less space than does asquare (or rectangular) cross-section:

$\begin{matrix}{{{2R^{2}} - {\frac{3\sqrt{3}}{4}R^{2}}} = \Delta} & \left( {{Eq}.6} \right)\end{matrix}$

which, when simplified is about 0.7 R².

Chip space “S”: the area not occupied by the endodontic instrumentwithin the circle of rotation, where A=a+S. For a triangular crosssection, the total chip space S is

$\begin{matrix}{{\Pi R^{2}} - {\frac{3\sqrt{3}}{4}R^{2}{or}}} & \left( {{Eq}.5} \right)\end{matrix}$ $\begin{matrix}{R^{2}\left( {\Pi - \frac{3\sqrt{3}}{4}} \right)} & \left( {{Eq}.6} \right)\end{matrix}$

The percentage of chip space S within the circle of rotation C beingabout 59%, calculated as follows:

$\begin{matrix}{\left( {1 - \frac{3\sqrt{3}}{4\Pi}} \right) \times 100} & \left( {{Eq}.7} \right)\end{matrix}$

that is 100%-41%. The chip space “s” between adjacent cutting edges is

$\begin{matrix}\frac{S}{n} & \left( {{Eq}.8} \right)\end{matrix}$

where n is the total number of cutting edges. For example, inembodiments of this disclosure, s=S/2. For a triangular cross-section,the chip space s between adjacent cutting edges is S/3:

$\begin{matrix}{\frac{1}{3}{R^{2}\left( {\Pi - \frac{3\sqrt{3}}{4}} \right)}} & \left( {{Eq}.9} \right)\end{matrix}$

which, when simplified, is about 0.61R². For a triangular cross-section,the percentage of chip space s occupying the circle of rotation C isabout 17% (i.e. 59%/3).

DETAILED DESCRIPTION

Referring to the drawings, embodiments of an endodontic instrument 10 ofthis disclosure have a cross-section that provides less torque strengthbut more flexibility than endodontic instruments of similar size,cutting angle, and material having a triangular-, square-, orrectangular-shaped cross-section. The endodontic instrument 10 of thisdisclosure includes a cross-section 11 along the length “L” between itshandle (proximal) end 15 and tip (distal) end 25 that occupies less ofthe total area “A” at each diameter than that occupied by a triangularcross-section.

In embodiments, the cross-section 11 at each diameter D1 to D16 of theinstrument 10 occupies less of the total area A than would a triangularcross-section at each diameter, where D1 is the diameter 1 mm from thetip end 25 and D16 is the diameter 16 mm from the tip end 25, therebeing intermediate diameters therebetween. This reduced cross-sectionalarea “a” provides an enlarged chip space “S”. In some embodiments, thecross-sectional area “a” occupies up to 39% to 40% of the total area Aat the handle end 15 and about 20%-25% at the tip end 25, the middlethird being about 30%-35%. The chip space “s” between adjacent cuttingedges 17 is greater than that between adjacent cutting edges of a priorart endodontic instrument having a triangular cross-section.

The endodontic instrument 10, which can be made of nickel-titanium andhave uniform taper along its entire blade or cutting length L, may beconfigured as a file or reamer. The instrument 10 may be configured forright-hand rotation or for left-hand reciprocation. When in use, theinstrument 10 shapes a root canal. Instrument size may be in range of 10to 35, there being subranges within this broader range. In someembodiments, the instrument size is 15, 20, 25 or 30.

In embodiments, only two helical-shaped flutes 13 spiral about thelength L to form only two cutting blades or edges 17. Embodiments do notinclude three or more cutting blades or edges. The cutting edges 17 arenon-landed other than for a portion located between the tip end 25 andD1. The cutting edges 17 may have a slightly negative rake angle orsubstantially neutral rake angle. The instrument's axis of rotationduring use may be the same as its longitudinal axis 19. Thecross-section 11 of the instrument 10 may be American football-shaped(prolate spheroid) having two opposing convex portions 21 intersectingat each cutting edge 17 or it may be wave-shaped, having a convexportion 21 intersecting an opposing concave portion 23 at each cuttingedge 17.

Compared to prior art endodontic instruments, the cutting edges 17 ofthis disclosure spiral over more of the cutting length L than do priorart instruments. In embodiments, the length L is at least 16 mm andincludes cutting edges along its entirety. The pitch—i.e., the distancebetween cutting edges 17 along the length L—is larger at the handle end15 than at the tip end 25, there being more spirals put unit lengthtoward the tip end 25 than toward the handle end 15. The total number ofspirals along the length L may be in a range of 6 to 8, the length Lbeing 16 mm, the instrument 10 being 25 mm in length from the handle tothe tip end 25. Depending on instrument size, the first 4 or 5 mm (D0 toD4 or D5) of the length L has more spirals that that of the last 4 of 5mm (D11 or D12 to D16), with the number of spirals in the intermediate 6to 8 mm providing a transition between the two.

In embodiments, the helical angle α of the spiral increases from thehandle end 15 to the tip end 25. The helical angle α at the tip end 25may be in a range of 40% to 75% greater than that at the handle end 15.For example, the helical angle α may in a range of 16° to 18° at ortoward the handle end 15, in a range of 26° to 30° at the tip end 25,and may be in a range of 22° to ° 24° in between. Similar to the numberof spirals, the increased helical angle α may be greater in the first 4to 5 mm.

The tip end 25 of the instrument is shovel-shaped, the shovel shapebeginning at about D2. The shovel shape includes slightly curved sides29 and a rounded tip 31. Between the D1 diameter and the tip end 25, thecutting edges 17 merge with the central core to form a radial land 27.The radial land 27 results from keeping a constant center core along theentire length L of the instrument 10. Therefore, there is no “sharp”transition angle of the cutting edges as would be understood by personsof skill in the art transitioning into the tip end 25.

While embodiments have been described, the scope of the invention isdefined by the following claims, the elements of which are entitled totheir full range of equivalents.

What is claimed:
 1. An endodontic instrument comprising: a tapered shafthaving a length L with diameters D0 to D16 along the length L, where D0is a diameter at a tip end of the endodontic instrument and D16 is adiameter 16 mm from the tip end; only two flutes spiraled about thelength L at a helical angle α to form two cutting edges, the two cuttingedges being non-landed between D2 and D16 and merging after D2 to form aland toward the tip end, the two cutting edges further forming a shovelblade beginning at D2 and ending at the tip end, the shovel blade havingcurved sides and the tip end being an end of the shovel blade androunded; a cross-section of the tapered shaft selected at each diameterD1 to D16 occupying less total area than 1.3 (Di/2)², where i is aninteger between 1 and 16, the cross-section lying in a plane orthogonalto a longitudinal axis of the endodontic instrument; the cross-sectionof the tapered shaft from D2 to D16 is asymmetrical wave-shape, theasymmetrical wave shape consisting of two waves opposing one another andintersecting at each cutting edge, each of the two waves having oneconcave portion and one convex portion, the one concave portion beingshorter than the one convex portion.
 2. The endodontic instrument ofclaim 1, wherein the helical angle α increases from the handle endtoward the tip end.
 3. The endodontic instrument of claim 2, wherein thehelical angle at the tip end is in a range of 10° to 12° greater thantoward the handle end.
 4. The endodontic instrument of claim 1, whereina number of spirals per unit length increases toward D0 from D16.
 5. Theendodontic instrument of claim 1, wherein a number of spirals per unitlength is greater between D0 and D5 than the number of spirals per unitlength between D11 and D16.
 6. The endodontic instrument of claim 1,wherein the cross-section has a circle of rotation having a diameter,wherein the two cutting edges lie on the diameter of the circle ofrotation.
 7. The endodontic instrument of claim 1, wherein, theendodontic instrument is configured for right-hand rotation.
 8. Theendodontic instrument of claim 1, wherein the endodontic instrument isin an ISO 3630-1 size range of 10 to
 35. 9. A method for reducinginstrument breakage during shaping of a root canal, the methodcomprising using the endodontic instrument of claim 1 during theshaping.